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Ultrafunctions and Generalized Solutions [PDF]
Advanced Nonlinear Studies, 2012 The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions.
V. Benci
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Generalized Solutions to a Chemotaxis-Navier-Stokes System with Arbitrary Superlinear Degradation [PDF]
SIAM Journal on Mathematical Analysis, 2021 Motivated by a recent work due to Winkler, we aim at investigating generalized solvability for the model the without imposing a critical superlinear exponent restriction on the logistic source function f .
Mengyao Ding, J. Lankeit
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The Role of Metaheuristics as Solutions Generators [PDF]
Symmetry, 2021 Optimization problems are ubiquitous nowadays. Many times, their corresponding computational models necessarily leave out of consideration several characteristics and features of the real world, so trying to obtain the optimum solution can not be enough for a problem solving point of view.
Hanane El Raoui +2 more
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When do Keller–Segel systems with heterogeneous logistic sources admit generalized solutions? [PDF]
Discrete & Continuous Dynamical Systems - B, 2020 We construct global generalized solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) + \lambda(x) u - \mu(x) u^\kappa,\\ v_t = \Delta v - v + u \end{cases} \end{align*} in smooth, bounded ...
Jianlu Yan, Mario Fuest
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Generalized Filippov solutions for systems with prescribed-time convergence [PDF]
at - Automatisierungstechnik, 2023 Dynamical systems with prescribed-time convergence sometimes feature a right-hand side exhibiting a singularity at the prescribed convergence time instant.
Richard Seeber
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Generalized solutions to models of compressible viscous fluids [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure.
A. Abbatiello, E. Feireisl, A. Novotný
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Generalized Weyl solutions [PDF]
Physical Review D, 2002 50 pages, 10 figures; v2: minor ...
Emparan García de Salazar, Roberto A. +1 more
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Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D [PDF]
Journal of Differential Equations, 2017 We study the chemotaxis–fluid system { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ ( n c ∇ c ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − n c , x ∈ Ω , t > 0 , u t + ∇ P = Δ u + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 , under homogeneous Neumann boundary conditions
Tobias Black
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Generalized solutions to models of inviscid fluids [PDF]
Discrete & Continuous Dynamical Systems - B, 2019 We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or ...
D. Breit, E. Feireisl, M. Hofmanová
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Optical and quantum electronics, 2023 In this study, Sardar sub-equation method is employed to obtain the solitary wave solutions for generalized fractional Tzitzéica type equations. By utilizing this method, novel solutions are derived for Tzitzéica, Tzitzéica Dodd–Bullough–Mikhailov and ...
Dean Chou +3 more
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